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8. Tsang, E.: Foundations of Constraint Satisfaction. Academic Press (1993) 9. Dechter, R.: Constraint Processing. Morgan Kaufmann (2003) 10. Subbarayan, S., Jensen, R.M., Hadzic, T., Andersen, H.R., Hulgaard, H., Møller, J.: Comparing two implementations of a complete and backtrack-free interactive configurator. In: CP'04 CSPIA Workshop. (2004) 97–111 11. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 8 (1986) 677–691 12. Meinel, C., Theobald, T.: Algorithms and Data Structures in VLSI Design. Springer (1998) 13. Wegener, I.: Branching Programs and Binary Decision Diagrams. Society for Industrial and Applied Mathematics (SIAM) (2000) 9

plausibility that a person is HIV positive and -1 indicating 100% plausibility of HIV negative. When training the rough set models using Markov Chain Monte Carlo, 500 samples were accepted and retained meaning that 500 sets of rules where each set contained 50 up to 550 numbers of rules with an average of 222 rules as can be seen in Figure 1. 500 samples were retained because the simulation had converged to a stationary distribution. This figure must be interpreted in the light of the fact on calculating the posterior probability we used the knowledge that fewer rules are more desirable than many. Therefore, the Bayesian rough set framework is able to select the number of rules in addition to the partition sizes. <image>

27. **Witlox, F., Tindemans, H., 2004. The application of rough set analysis in activity** based modeling: Opportunities and constraints. Expert Systems with Applications, 27, 585-592.

[14] T. Schiex, H. Fargier, G. Verfaillie, Valued Constraint Satisfaction Problems: Hard and Easy Problems, in: *Proc. IJCAI-95***, Montreal, Quebec,** Morgan Kaufmann, San Mateo, CA, 1995, pp.631-639. [15] L. Shapiro and R. Haralick, Structural descriptions and inexact matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 3**(1981)** 504-519.

The biases in equation 12 may be absorbed into the weights by including extra input variables set permanently to 1 making x 0 = 1 and z 0 = 1 , to give: $$y_{{}_{k}}=f_{\rm outer}\Biggl{(}\sum_{j=0}^{M}\gamma_{{}_{k}}(G_{{}_{x}},R,N_{{}_{r}})_{{}_{kj}}f_{\rm inner}\Biggl{(}\sum_{i=0}^{d}w_{ji}^{(i)}x_{i}\Biggr{)}\Biggr{)}\tag{13}$$ The function fouter( ) may be logistic, linear, or sigmoid while finner is a hyperbolic tangent function. The equation may be represented schematically by Figure 1. <image>

<image> The average accuracy achieved was 62%. This accuracy can be compared with the accuracy of Bayesian multi-layered perceptron trained using hybrid Monte Carlo by Tim and Marwala (2006), which gave the accuracy of 62%, and Bayesian rough sets by Marwala and Crossingham (2007), which gave the accuracy of 58%, all on the same database. The results show that the incorporation of rough sets into the multi-layered perceptron neural network to form neuro-rough model does not compromise on the results obtained from a traditional Bayesian neural network but it added a dimension of rules. When the interaction between the neural network and the rough set components was conducted by analysing the average magnitudes of the weights ( w ) and the

magnitudes of the γ **which is the output of the rough set model, it was found that the** rough set model contributes (average γ **of 0.43) to the neuro-rough set model less than** the neural network component (average w **of 0.49). The receiver operator characteristics** (ROC) curve was also generated and the area under the curve was calculated to be 0.59 and is shown in Figure 4. This shows that the neuro-rough model proposed is able to estimate the HIV status. <image> Training neuro-rough model with Bayesian framework allows us to determine how confident we are on the HIV status we predict. For example, Figure 5 shows that the average HIV status predicted is 0.8 indicating that a person is probably HIV positive.

<image> The goal of the learning algorithm as proposed by (Vapnik and Lerner, 1963), is to find the hyperplane with maximum margin of separation from the class of separating hyperplanes. But since real-world data often exhibit complex properties, which cannot be separated linearly, more complex classifiers are required. In order to avoid the complexity of the nonlinear classifiers, the idea of linear classifiers in a feature space comes into place. Support vector machines try to find a linear separating hyperplane by first mapping the input space into a higher dimensional feature space F. This implies each training example xi **is substituted with** Ф(xi) Yi((w. Ф(xi) +b), i=1,2,…n (6)

<image> **Fig. 2(a). Chamoli Earthquake at Barkot in NE direction** Peak Acceleration = 0.16885m/sec/sec <image> Fig. 2(b) Uttarkashi Earthquake at Barkot in NE direction Peak Acceleration : 0.9317m/sec/sec <image> <image>

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<image> Fig. 5(a). 120% Response Comparison Between Neural and Desired of Chamoli Earthquake at Barkot (NE) (748 points) ω=0.01 (After training from 550 points) <image> Time Fig. 5(b). 80% Response Comparison Between Neural and Desired of Chamoli Earthquake at Barkot (NE) (748 points) ω**=0.5** (After training from 550 points)

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[37] L. L. Thurstone. *The nature of intelligence*. Routledge, London, 1924. [38] P. Voss. Essentials of general intelligence: The direct path to AGI. In B. Goertzel and C. Pennachin, editors, *Artificial General Intelligence*. SpringerVerlag, 2005. [39] P. Wang. On the working definition of intelligence. Technical Report 94, Center for Research on Concepts and Cognition, Indiana University, 1995. [40] D. Wechsler. *The measurement and appraisal of adult intelligence*. Williams & Wilkinds, Baltimore, 4 edition, 1958. [41] R. M. Yerkes and A. W. Yerkes. *The great apes: A study of anthropoid life*. Yale University Press, New Haven, 1929.

<image> <image> The innovation rate and the number of new better fitnesses found **along the** longest neutral random walk for each NN **is given in figure 8. The majority of** new fitness value found along random walk is deleterious, very few solutions are fitter. This study give us a better description of Majority fitness landscape neutrality which have important consequence on metaheuristic design. The **neutral** degree is high. Therefore, the selection operator should take into **account the** case of equality of fitness values. Likewise the mutation rate and population size should fit to this neutral degree in order to find rare good solutions outside NN [42]. For two potential solutions x and y on NN**, the probability** p that at least one solution escaped from NN is P(x 6∈ NN ∪ y 6∈ NN) =

Although all EH seem to have roughly the same shape (see fig. 10), we can ask whether flipping one particular bit changes the fitness in the same way. For instance, for all the optima, flipping the first bit from '0' to '1' causes a drop in fitness. More generally, flipping each bit, we compute the average and standard deviation of the difference in fitnesses; results are sorted into increasing average differences (see figure 13-a). The bits which are the more deleterious are the ones with the smaller standard deviation, and as **often** as not, are in the schemata S. So, the common bits in the blok **seem to be** important to find good solution: for a metaheuristic, it would be of benefit to search in the subspace defined by the schema S.

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blok′(see figure 12) are shorter than the one between C and the blok**. The six** blok′**are more concentrated around** C ′ **. Note that, although Coe1 and Coe2** are the highest local optima, they are the farthest from C ′ , **although above** distance 38.**5 which is the average distance between** C ′ **and a random point in** the Olympus landscape. This suggest one should search around the **centroid** while keeping one's distance from it. <image> <image> The figure 13-b shows the average and standard deviation over the six **blok**′ of evolvability per bit. The one over blok′**have the same shape than the mean** curve over blok, only the standard deviation is different, on the average standard deviation is 0.08517 for blok and 0.08367 for blok′**. The Evolvability** Horizon is more homogeneous for the blok′than for the **blok**.

GLK′**-0.15609 -0.19399** Davis′**-0.05301 -0.15103** Das′**-0.09202 -0.18476** ABK′**-0.23302 -0.23128** Coe1′**-0.01087 0.077606** Coe2′**-0.11849 -0.17320** nearest -0.16376 -0.20798 C ′ **-0.23446 -0.33612** <image> ## 5.2.3 Correlation Structure Analysis: Arma Model In this section we analyze the correlation structure of the Olympus **landscape** using the Box-Jenkins method (see section 3.3.4). The starting solution of each random walk is randomly chosen on the Olympus. At each step one random bit is flipped such that the solution belongs to the Olympus and the fitness is computed over a new sample of ICs of size 104**. Random walks have length** 104 **and the approximated two-standard-error bound used in the Box-Jenkins**

[42] L. Barnett, Netcrawling - optimal evolutionary search **with neutral networks,** in: Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, IEEE Press, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 2001, pp. 30–37. [43] L. Altenberg, The evolution of evolvability in genetic **programming, in: K. E.** Kinnear, Jr. (Ed.), Advances in Genetic Programming, MIT Press, 1994, Ch. 3, pp. 47–74.

[15] L. Ruschendorf. Convergence of the iterative proportional fitting procedure. *Annals Stat.*, 23, 1995. [16] V. Kolmogorov. Convergent tree-reweighted message passing for energy minimization. IEEE Trans. Pattern Analysis and Machine Intelligence, January 2005. [17] D. Malioutov, J. Johnson, and A. Willsky. Walk-sums and belief propagation in Gaussian graphical models. J. Machine Learning Research, 7, October 2006. [18] V. Chandrasekaran, J. Johnson, and A. Willsky. Estimation in Gaussian graphical models using tractable subgraphs: a walk-sum analysis. IEEE Trans. Signal Processing, to appear. [19] B. Gidas. A renormalization group approach to image processing problems. *IEEE Trans. Pattern Analysis and Machine Intelligence*, 11, February 1989. [20] U. Trottenberg, C. Oosterlee, and A. Schuller. *Multigrid*. Academic Press, 2001.

<image> Analyzing covert social network foundation behind terrorism disaster Figure 9 shows F value gain to retrieve the records where a covert conspirator, Raed Hijazi, has been hidden. Iav(b,) and Itp(b,) are employed again as in Figure 5. Itp(b,) shows better performance although it is still a little unstable and may not be sufficient for a practical use. The performance may be improved by focusing on the relationship between 2 clusters, rather than between the all clusters. <image>

Y. Maeno and Y. Ohsawa <image> <image> The overall network topology is studied. The nodal degree averaged over the all nodes is μ( d ) = 4.6 . Gini coefficient of the nodal degree is 0.33. The clustering coefficient averaged over the all nodes is μ (c) = 0.6 . It is 3.2 times larger than that in the Barabasi-albert model (Barabasi, 1999), a scale-free network, having the same Gini coefficient. Large clustering coefficient indicates that clusters exist as a core structure, but the network takes a less compact form. As qualitatively suggested by (Klerks, 2002), the terrorists possess a cluster-and-bridge structure, rather than a center-and-periphery

# Node Discovery Problem For A Social Network Yoshiharu Maeno ∗ Social Design Group ## Abstract Methods to solve a node discovery problem for a social network are presented. Covert nodes refer to the nodes which are not observable directly. They transmit the influence and affect the resulting collaborative activities among the persons in a social network, but do not appear in the surveillance logs which record the participants of the collaborative activities. Discovering the covert nodes is identifying the suspicious logs where the covert nodes would appear if the covert nodes became overt. The performance of the methods is demonstrated with a test dataset generated from computationally synthesized networks and a real organization. arXiv:0710.4975v2 [cs.AI] 7 Aug 2009 1

<image> (the lower bound). The vertical solid line indicates the position where D r = D t . <image> <image> <image> <image> <image>

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## 6.1. Extensionalization In order to make the system tractable at run time, we implemented an offline technique to speed up the program. We modified SWORIER to extensionalize all of the facts that can be derived from the input (that a user might want to query on), converting the program from an intensional form to an extensional form. Figure 5 shows the modified system design. <image>

Berkeley, Technical report no. UCB/CSD 90/600, U. C. Berkeley Computer Science Division. Also: *Fast Logic Program Execution*, Intellect Books. Van Roy, Peter & Despain, Alvin M. (1992), "High-Performance Logic Programming with the Aquarius Prolog Compiler", *IEEE Computer*, 25(1):54-68. Van Roy, Peter (1994), "The Wonder Years of Sequential Prolog Implementation", *Journal of* Logic Programming, 19:385-441. [Online at ftp://ftp.digital.com/pub/DEC/PRL/researchreports/PRL-RR-36.ps.Z, accessed 12 Sep 2007]. Raphael Volz (2004), *Web Ontology Reasoning with Logic Databases*, PhD thesis, AIFB, University of Karlsruhe. Volz, Raphael, Decker, Stefan & Oberle, Daniel (2003), "Bubo - Implementing OWL in RuleBased Systems", http://www.daml.org/listarchive/joint-committee/att-1254/01-bubo.pdf [Accessed 12 Sep 2007].

10 **Adamatzky et al** <image> ## 7. Conclusion We have hybridized the paradigm of reaction-diffusion cellular automata 4,21,5 **with** evolutionary techniques of breeding glider-supporting rules 13,14,15,16 **to statistically evaluate the set of all possible totalistic cell-state transition functions which** support mobile and stationary localizations. We calculated exact structures of glider likehood matrices and interpreted them in terms of abstract reactions. We demonstrated that quasi-chemical systems derived from glider-supporting rules exhibit classical dynamics of excitable chemical systems. We obtained computational experiment evidences that by reducing glider likehood matrices to their **strong components we obtain a set of local transition rules that exhibit exclusively stationary** localizations. Results of the research undertaken provide a priceless tool for designing collision-based computing schemes in spatially extended non-linear **systems.** ## References

<image> Evolving localizations in reaction-diffusion cellular automata 5

<image> Evolving localizations in reaction-diffusion cellular automata 7 molecules B **does not exceed four.** Finding 3. Reactant B **is more likely to be produced during quasi-chemical reactions** derived from F**-matrices.**

# Convergence Of Expected Utilities With Algorithmic Probability Distributions PETER DE BLANC DEPARTMENT OF MATHEMATICS TEMPLE UNIVERSITY

CONVERGENCE OF EXPECTED UTILITIES WITH ALGORITHMIC PROBABILITY DISTRIBUTIONS3 References [1] Kleene, S., **On Notation for Ordinal Numbers**, The Journal of Symbolic Logic, 3 (1938), 150-155. [2] Hutter, M., **Universal Algorithmic Intelligence: A mathematical top-down approach**, Artificial General Intelligence (2007), Springer [3] Rad´o, T., **On non-computable functions**, Bell Systems Tech. J. 41, 3 (May 1962).

TOTh 2007 : « Terminologie & Ontologie : Théories et Applications » - Annecy 1er **juin 2007** Terminologie et ontologie**. Roche C. Revue Langages n°157, pp. 48-62. Editions Larousse,** mars 2005. Ontology Learning from Text: Methods, Evaluation and Applications. **Frontiers in Artificial** Intelligence and Applications, Vol. 123. Edited by Buitelaar P., Cimiano P., Magnini B., Ios Press Publication, July 2005. Text analysis for ontology and terminology engineering**. Aussenac-Gilles N., Soergel D.** Applied Ontology. n°1. pp. 35-46, 2005. Ontology for long-term knowledge**. Dourgnon-Hanoune A., Salaün P., Roche C. XIX** IEA/AIE, Annecy 27-30 June 2006. Dire n'est pas Concevoir**. Christophe Roche. 18èmes journées francophones d' « Ingénierie** des Connaissances », Grenoble 4-6 juillet 2007.

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To tackle the problem in practice, six important questions should be addressed, constituting the "six layers of resistance to change". These questions can be used to trigger discussions (Goldratt Institute 2001, 6): (1) Has the right problem been identified? (2) Is this solution leading us in the right direction? (3) Will the solution really solve the problems? (4) What could go wrong with the solution? Are there any negative side-effects? (5) Is this solution implementable? (6) Are we all really up to this? <image> Fig. 2. The Current Reality Tree (CRT) represents the core problem underneath this paper (how to make the indefinite continuation of life possible?). The "injection" (grayed) is the proposition which is challenged. It is the statement that [a] : "intelligent civilization can not have any significant influence on cosmic evolution".

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# Reflective Visualization And Verbalization Of Unconscious Preference Yoshiharu Maeno ∗**and Yukio Ohsawa** † October 25, 2018 ## Abstract A new method is presented, that can help a person become aware **of his or her unconscious preferences,** and convey them to others in the form of verbal explanation. The method combines the concepts of reflection, visualization, and verbalization. The method was tested in **an experiment where the unconscious preferences** of the subjects for various artworks were investigated. In the experiment, two lessons were learned. The first is that it helps the subjects become aware of their unconscious preferences to verbalize weak preferences as compared with strong preferences through discussion over preference diagrams. The second is that it is effective to introduce an adjustable factor into visualization to adapt to the differences in the subjects and to foster their mutual understanding. ## 1 Introduction 1

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Nevertheless, we notice from table 1 that the takeover times are not similar for αo and ro. Consequently, the selective pressure induced on the population is different for the two algorithms. The observations on figure 7 are in adequation with this: The algorithm with stochastic tournament preserves more genotypic diversity for the threshold value than the one with anisotropic selection. The genotypic diversity measures were made on instance nug30 for which the cGA with stochastic tournament selection obtains the best performance. However, results on diversity put in evidence properties of the selection operators which are independant from the instance tested. The selective pressure is related to the exploration/exploitation trade-off. We conclude from the results presented in table 1 and figure 6 that studying the exploration/exploitation trade-off is insufficient to explain performance of cellular genetic algorithms. In cGAs, the grid topology structures the search dynamic.

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<image> a β =1.01 <image>

<image> Some results of the proposed algorithm can be highlighted as follows: <image> 1-Detection of membership functions (MFs) for any input and output (figure 4) 2-The dominated rules in if-then format between inputs and output (safety factor for any block) 3-Possible damage parts around tunnel. In similar conditions; a compression between DDA (discontinuous deformation analysis)-MacLaughlin&Sitar.1995- and results of mentioned algorithm has been accomplished. See figure5. <image>

<image> input 1 <image> input2 input3 <image> Dec

<image> We also apply the term-based (as opposed to relation-based) subsumption approach [4] on the dataset we collected. In particular, we tokenize and normalize collection and set names as the same way we did before. For each set, we aggregate its terms and collection terms together as a document (a bag of concepts). We hypothesize that terms used in collection names are more prevalent (and thus have high centrality) - and subsume - terms from set names. We then use subsumption approach with the threshold specified in [4]. The hierarchies produced by this approach are much sparser and contain fewer informative concepts than the folksonomy learned by our approach. We also tried to relax subsumption threshold in steps from 0.8 to 0.55; yet many informative concepts and relations were still discarded. One reason why subsumption approach does not work very well in this context is that a certain concept usually relates to many other concepts. Thus, it is

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level set methods, IEEE Oceans'05 Europe, Brest, France**, 20-23 June 2005.** [12] A. Appriou, Situation Assessment Based on Spatially Ambiguous Multisensor Measurements, International Journal of Intelligent Systems**, Vol 16,** No 10, pp. 1135-1166, 2001. [13] T. Denoeux, A k-nearest neighbor classification rule based on Dempster-Shafer Theory, IEEE Transactions on Systems, Man and Cybernetics, Vol 25, No 5, pp. 804-913, 1995. [14] Ph. Smets, The Combination of Evidence in the Transferable Belief Model, IEEE Transactions on Pattern Analysis and Machine Intelligence**, Vol** 12(5), pp 447-458, 1990. [15] Ph. Smets, Constructing the pignistic probability function in a context of uncertainty, Uncertainty in Artificial Intelligence, Vol 5, pp 29-39, 1990.

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between RQD& lugeon) are satisfied, but in other <image> zones, the said rule is disregarded. To finding out of the background on these major zones, we refer to the clustered data set by 2D SOM with 7*9 weights in competitive layer (figure 10-c), on the first set of the attributes. The clustered and graphical estimation disclose suitable coordination, relatively. For example in figure 13-b, we have highlighted three distinctive patterns among lugeon and Z, RQD, TWR. One of the main reasons of being such patterns in the investigated rock mass is in the definition of RQD. In measurement of RQD, the direction of joints has not been considered, so that the rock masses with appropriate joints may follow high RQD. <image> <image> <image> <image> The roles of uncertainty and vague information in geomechnaics analysis are undeniable features.

<image> <image> Figure 17 shows the variation of the lugeon data in Z*= {1} to {5} which has been acquired by serving five condition attributes in RST (figure 16; the symbolic values by 1-D SOM -5 neurons). The categories 1 to 5 state: very low, low, medium,

Ontology-based Knowledge Management System for Industry Cluster 5 <image> The feasibility study serves as decision support for an economical, technical and project feasibility study, in order to select the most promising focus area and target solution. This phase identifies problems, opportunities and potential solutions for the organization and environment. Most of the knowledge engineering methodologies provide the analysis method to analyze the organization before the knowledge engineering process. This helps the knowledge engineer to understand the environment of the organization. CommonKADS also provides context levels in the model suite (figure 1.2) in order to analyze organizational environment and the corresponding critical success factors for a knowledge system [16]. The organization model provides five worksheets for analyzing feasibility in the organization as shown in figure 1.4. ## 3.1 Feasibility Study Phase <image>

<image> mc(∅) = 2xy, mc(A) = x + y − 2xy − xz = x − mc(∅) + y(1 − x), mc(B) = x + y − xy − 2xz = x − mc(∅) + z(1 − x), mc(Θ) = 1 − 2x − y − z + 2xy + 2xz. Therefore, as 1 − x ≥ 0: $$m_{c}(A)>m_{c}(B)\iff y>z.$$ $$\mathrm{R~yields:}$$ The PCR yields: mP CR(∅) = 0 mP CR(A) = x − mc(∅) + y(1 − x) + x 2z x + z +xy2 x + y mP CR(B) = x − mc(∅) + z(1 − x) + xz2 x + z +x 2y x + y mP CR(Θ) = 1 − 2x − y − z + 2xy + 2xz. , , So, we have: $$(m_{PCR}(A)+m_{c}(\emptyset)-x)(x+y)(x+z)=y(1-x)(x+z)(x+y)$$ $$+x^{2}z(x+y)+y^{2}x(x+z)$$ $$=y(x+y)(x+z)+x^{3}(z-y)$$ (mP CR(B) + mc(∅) − x)(x + y)(x + z) = z(x + y)(x + z) − x 3(z − y),

mP CR(A) > mP CR(B) ⇐⇒ (y − z)((x + y)(x + y) − 2x 3) > 0. As 0 ≤ x ≤ 1 2 , we have 2x 3 ≤ x 2 ≤ (x + y)(x + z). So mP CR(A) > mP CR(B**) if** and only if **y > z**. That shows that the stability of the decision is reached if a1 = b1 **for all** a2 and b2 ∈ [0, 1] or by symmetry if a2 = b2 for all a1 and b1 ∈ [0, 1]. 4.3.2 Case a1 = b2 In this situation, expert 1 believes A and the expert 2 believes B **with the same** weight: <image> <image> Figure 3: Decision changes, projected on the plane a1, b2. The conjunctive rule yields: mc(∅) = x 2 + yz, mc(A) = x + z − xz − mc(∅) = −x 2 + x(1 − z) + z(1 − y), mc(B) = x + y − xy − mc(∅) = −x 2 + x(1 − y) + y(1 − z), mc**(Θ) = 1 +** mc(∅) − 2x − y − z + x(y + z). Therefore: $$m_{c}(A)>m_{c}(B)\iff(x-1)(y-z)>0,$$ as 1 − x ≥ 0: mc(A) > mc(B) ⇐⇒ **y > z.** $\lambda=u\lambda>0$

The PCR yields: mP CR(∅**) = 0**, $$m_{P C R}(A)=x+z-x z-m_{c}(\emptyset)=-x^{2}+x(1-z)+z(1-y)+\frac{x^{3}}{2x}+\frac{y z^{2}}{y+z}.$$ , $$m_{PCR}(B)=x+y-xy-m_{c}(\emptyset)=-x^{2}+x(1-y)+y(1-z)+\frac{x^{3}}{2x}+z$$ $$m_{PCR}(\Theta)=1+m_{c}(\emptyset)-2x-y-z+x(y+z).$$ +y y + z , $$\underline{{y^{2}z}}$$ Therefore: mP CR(A) > mP CR(B) ⇐⇒ (y − z) ((x − 1)(y + z) − yz) > 0, as (x − 1) ≤ 0, (x − 1)(y + z) − yz ≤ **0 and:** mP CR(A) > mP CR(B) ⇐⇒ **y > z.** That shows that the stability of the decision is reached if a1 = b2 for all a2 and b1 ∈ [0, 1] or by symmetry if a2 = b1 for all a1 and b2 ∈ [0, 1]. 4.3.3 Case a2 = 1 − a1 We can notice that if a1 + a2 > **1, no change occurs. In this situation, we have** <image> b1 + b2 < **1, but calculus is still to be done.** In this situation, if a2 = 1 − a1: <image>

## Appendix: Algorithms An expert e **is an association of a list of focal classes and their masses. We** write size(e) the number of its focal classes. The focal classes are e[1], e**[2], . . . ,** e[size(e)]. The mass associated to a class c is e(c**), written with paranthesis.** Data: n experts ex: ex[1] **. . . ex**[n] Result: Fusion of ex by Dubois-Prade method : edp for i *= 1 to* n do foreach c in ex[i] do Append c to cl[i]; foreach ind *in [1, size(*cl[1])] × *[1, size(*cl[2])] × . . .× *[1, size(*cl[n])] do s ← Θ; for i *= 1 to* n do s ← s ∩ cl[i][ind[i]]; if s = ∅ **then** lconf ← 1; u ← ∅; for i *= 1 to* n do u ← p ∪ cl[i][ind[i]]; lconf ← lconf × ex[i](cl[i][ind[i**]]);** edp(u) ← edp(u) + **lconf**; else lconf ← 1; for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** edp(s) ← edp(s) + **lconf**;

Data: n experts ex: ex[1] **. . . ex**[n] Result: Fusion of ex **by PCR5 method :** ep for i *= 1 to* n do foreach c in ex[i] do Append c to cl[i]; foreach ind *in [1, size(*cl[1])] × *[1, size(*cl[2])] × . . .× *[1, size(*cl[n])] do s ← Θ; for i *= 1 to* n do s ← s ∩ cl[i][ind[i]]; if s = ∅ **then** lconf ← 1; el **is an empty expert;** for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** if cl[i][ind[i]] in el **then** el(cl[i][ind[i]]) ← el(cl[i][ind[i]]) ∗ ex[i](cl[i][ind[i**]]);** else el(cl[i][ind[i]]) ← ex[i](cl[i][ind[i**]]);** for c in el do sum ← sum + el(c); for c in el do ep(c) ← ep(c) + g(el(c)) ∗ **lconf /sum**; else lconf ← 1; for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** ep(s) ← ep(s) + **lconf**;

Data: n experts ex: ex[1] **. . . ex**[n] Data**: A non-decreasing positive function** f Result: Fusion of ex by PCR6f **method :** ep for i *= 1 to* n do foreach c in ex[i] do Append c to cl[i]; foreach ind *in [1, size(*cl[1])] × *[1, size(*cl[2])] × . . .× *[1, size(*cl[n])] do s ← Θ; for i *= 1 to* n do s ← s ∩ cl[i][ind[i]]; if s = ∅ **then** lconf ← 1; sum ← 0; for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** sum ← sum + f(ex[i](cl[i][ind[i**]]));** for i *= 1 to* n do ep(ex[i][ind[i]]) ← ep(ex[i][ind[i]]) + f(ex[i](cl[i][ind[i**]]))** ∗ lconf /sum; else lconf ← 1; for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** ep(s) ← ep(s) + **lconf**;

Data: n experts ex: ex[1] **. . . ex**[n] Data**: A non-decreasing positive function** g Result: Fusion of ex by PCR6g **method :** ep for i *= 1 to* n do foreach c in ex[i] do Append c to cl[i]; foreach ind *in [1, size(*cl[1])] × *[1, size(*cl[2])] × . . .× *[1, size(*cl[n])] do s ← Θ; for i *= 1 to* n do s ← s ∩ cl[i][ind[i]]; if s = ∅ **then** lconf ← 1; el **is an empty expert;** for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** el(cl[i][ind[i]]) ← el(cl[i][ind[i]]) + ex[i](cl[i][ind[i**]]);** sum ← 0; for c in el do sum ← sum + g(el(c)); for c in el do ep(c) ← ep(c) + g(el(c)) ∗ **lconf /sum**; else lconf ← 1; for i *= 1 to* n do lconf ← lconf × ex[i](cl[i][ind[i**]]);** ep(s) ← ep(s) + **lconf**;

bramble bush by clarifying the concepts. Iowa Law Review 73, 1001–1077. Wright, R. W. (2001). Once more into the bramble bush: Duty, causal contribution, and the extent of legal responsibility. *Vanderbilt Law Review 54*(3), 1071– 1132.

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[9] F. Murtagh, Editorial, Computer Journal, in press, 2008. doi:10.1093/comjnl/bxn008 [10] C.J. van Rijsbergen, The Geometry of Information Retrieval, Cambridge University Press, 2004.

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%% function [elemC,cmp]=treat(focal,Theta) nbelem=size(focal,2); PelemC=0; oper=0; e=1; if nbelem while e <= nbelem elem=focal(e); switch elem case -1 oper=-1; case -2 oper=-2; case -3 [elemC,nbe]=treat(focal(e+1:end),Theta); e=e+nbe; if oper~=0 & ~isequal(PelemC,0) elemC=eval(oper,PelemC,elemC); oper=0; end PelemC=elemC; case -4 cmp=e; e=nbelem; otherwise elemC=Theta{elem}; if oper~=0 & ~isequal(PelemC,0) elemC=eval(oper,PelemC,elemC); oper=0; end PelemC=elemC; end e=e+1; end else elemC=[]; end end Function 6 - codingExpert function function [expertC]=codingExpert(expert,Theta) % Code the focal element for DSmT framework %

[res]=Mix(expertC); case 11 % DPCR (Martin and Osswald criterium) [res]=DPCR(expertC); case 12 % MDPCR (Martin and Osswald criterium) [res]=MDPCR(expertC); case 13 % Zhang's rule [res]=Zhang(expert) otherwise 'Accident: in combination choose of criterium: uncorrect' end ## Function 8 - Conjunctive Function function [res]=conjunctive(expert) % Conjunctive Rule % % [res]=conjunctive(expert) % % Inputs: % expert = containt the structures of the list of focal element and % corresponding bba for all the experts % % Output: % res = is the resulting expert (structure of the list of focal % element and corresponding bba) % % Copyright (c) 2008 Arnaud Martin nbexpert=size(expert,2); for i=1:nbexpert nbfocal(i)=size(expert(i).focal,2); nbbba(i)=size(expert(i).bba,2); if nbfocal(i)~=nbbba(i) 'Accident: in conj: the numbers of bba and focal element... are different' end end interm=expert(1); for exp=2:nbexpert nbfocalInterm=size(interm.focal,2); i=1; comb.focal={}; comb.bba=[];

expertDec.focal=elemDecC; expertDec.bba=zeros(1,size(elemDecC,2)); for foc=1:size(expert.focal,2) ind=findeqcell(elemDecC,expert.focal{foc}); if ~isempty(ind) expertDec.bba(ind)=expert.bba(foc); else expertDec.bba(ind)=0; end end case '2T' type=0; natoms=size(Theta,2); expertDec.focal(1)={[]}; indFoc=findeqcell(expert.focal,{[]}); if isempty(indFoc) expertDec.bba(1)=0; else expertDec.bba(1)=expert.bba(indFoc); end step =2; for i=1:natoms expertDec.focal(step)=codingFocal({[i]},Theta); indFoc=findeqcell(expert.focal,expertDec.focal{step}); if isempty(indFoc) expertDec.bba(step)=0; else expertDec.bba(step)=expert.bba(indFoc); end step=step+1; indatom=step; for step2=2:indatom-2 expertDec.focal(step)={[union(expertDec.focal{step2},... expertDec.focal{indatom-1})]}; indFoc=findeqcell(expert.focal,expertDec.focal{step}); if isempty(indFoc) expertDec.bba(step)=0; else expertDec.bba(step)=expert.bba(indFoc); end step=step+1; end end elemDecC=expertDec.focal;

% % Inputs: % focal = one focal element (matrix) % listFocal = the list of elements in Theta (all different) % % Output: % bool = boolean: true if focal is in listFocal, elsewhere false % % Copyright (c) 2008 Arnaud Martin n=size(listFocal,2); bool=false; for i=1:n if isequal(listFocal{i},focal) bool=true; break; end end end %% function [decFocElem]=MaxFoc(funcDec,elemDecC,type) fieldN=fieldnames(funcDec); switch fieldN{2} case 'BetP' funcDec.bba=funcDec.BetP; case 'Bel' funcDec.bba=funcDec.Bel; case 'Pl' funcDec.bba=funcDec.Pl; case 'DSmP' funcDec.bba=funcDec.DSmP; end if type [funcMax,indMax]=max(funcDec.bba); FocMax={funcDec.focal{indMax}}; else nbFocal=size(funcDec.focal,2); TabSing=[]; for foc=1:nbFocal if isElem(funcDec.focal{foc}, elemDecC) TabSing=[TabSing [foc ; funcDec.bba(foc)]]; end end [funcMax,indMax]=max(TabSing(2,:)); FocMax={funcDec.focal{TabSing(1,indMax)}};

end if funcMax~=0 decFocElem.focal=FocMax; switch fieldN{2} case 'BetP' decFocElem.BetP=funcMax; case 'Bel' decFocElem.Bel=funcMax; case 'Pl' decFocElem.Pl=funcMax; case 'DSmP' decFocElem.DSmP=funcMax; end else decFocElem=-1; end end Function 12 - findFocal function function [elemDecC]=findFocal(Theta,minSpe,maxSpe) % Find the element of DTheta with the minium of specifity minSpe % and the maximum maxSpe % % [elemDecC]=findFocal(Theta,minSpe,maxSpe) % % Input: % Theta = list of coded (and eventually reduced with constraint) of % the elements of the discernment space % minSpe = minimum of the wanted specificity % minSpe = maximum of the wanted specificity % % Output: % elemDec = list of elements on which we want to decide with the % minimum of specifity minSpe and the maximum maxSpe % % Copyright (c) 2008 Arnaud Martin elemDecC{1}=[]; n=size(Theta,2); ThetaSet=[]; for i=1:n ThetaSet=union(ThetaSet,Theta{i}); end for s=minSpe:maxSpe

step =1; for i=1:n basetmp(step)={[Theta{i}]}; step=step+1; indatom=step; for step2=1:indatom-2 basetmp(step)={intersect(basetmp{indatom-1},basetmp{step2})}; step=step+1; end end sBaseTmp=size(basetmp,2); step=1; for i=1:sBaseTmp if ~isempty(basetmp{i}) base(step)=basetmp(i); step=step+1; end end sBase=size(base,2); DTheta{1}=[]; step=1; nbC=2; stop=0; D_n1 =[0 ; 1]; sDn1=2; for nn=1:n D_n =[ ] ; cfirst=1+(nn==n); for i =1:sDn1 Li=D_n1(i,:); sLi=size(Li,2); if (2*sLi>sBase)&& (Li(sLi-(sBase-sLi))==1) stop=1; break end for j=i:sDn1 Lj=D_n1(j,:); if(and(Li,Lj)==Li)&(or(Li,Lj)==Lj) D_n=[D_n ; Li Lj ] ; if size(D_n,1)>step step=step+1; DTheta{step}=[]; for c=cfirst:nbC if D_n(end,c) if isempty(DTheta{step}) DTheta{step}=base{sBase+c-nbC}; else

[34] Ph. Smets. Decision making in the tbm: the necessity of the pignistic transformation. *International Journal of Approximate Reasonning*, 38:133– 147, 2005. [35] Ph. Smets. Analyzing the combination of conflicting belief functions. *Information Fusion*, 8:387–412, 2006. [36] B. Tessem. Approximations for efficient computation in the theory of evidence. *Artificial Intelligence*, 61:315–329, 1993. [37] F. Voorbraak. A computationally efficient approximation of dempstershafer teory. *International Journal Man-Machine Studies*, 30:525–536, 1989. [38] N. Wilson. Algorithms for Dempster-Shafer theory. In D.M. Gabbay and Ph. Smets, editors, *Hanbook of defeqsible reasoning and uncertainty management*, volume 5: Algorithms for uncertainty and Defeasible Reasoning, pages 421–475. Kluwer Academic Publisher, Boston, 2000.

<image> W - World W * - Mata-Knowledge M - Modeller M* - Introspective Knowledge

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<image> exocomportamiento posicional con un punto de color verde y un exocomportamiento sensible de color azul. Los diagramas que contienen comportamientos aleatorios, posicionales y sensibles son disjuntos entre ellos. Por otro lado el resto de puntos tiene un color que es combinaci´on de los tres colores primarios, representando que ese exocomportamiento es combinaci´on de los tres tipos de car´acter de la fasa. El diagrama que aparece se muestra en la figura 1. Antes de terminar este apartado se debe aclarar una cuesti´on para comprender exactamente cu´ales son los elementos que contiene el conjunto de

| Nonconjunction, not | | | | | | |-----------------------|-----|----|-----------------------|----|-----------------------------------------| | 1 2 | | | | | | | 1−t t | x ∨ | ∧ | ∧ | | | | yx | yx | yx | y | | | | , | , | , | | | ∧ | both…and; "nand" Affirmation; validity; | | 1 | 1 | T | tautology; constant 1 | | | 7

based approach for a flowshop scheduling problem", *Annals of Operations Research*, 63, 397–414. Pinedo, M. (2002), *Scheduling: Theory, Algorithms, and Systems*, Upper Saddle River, NJ: Precentice Hall. Reeves, C.R. (1999), "Landscapes, operators and heuristic search", *Annals of Operations Research*, 86, 473–490. Taillard, E. (1993), "Benchmarks for basic scheduling problems", *European Journal of Operational Research*, 64, 278–285. T'kindt, V. and Billaut, J.-C. (2002), *Multicriteria Scheduling: Theory, Models and Algorithms*, Berlin, Heidelberg, New York: Springer Verlag. Ulungu, E.L., Teghem, J., Fortemps, P.H. and Tuyttens, D. (1999), "MOSA method: A tool for solving multiobjective combinatorial optimization problems", *Journal of Multi-Criteria Decision Making*, 8, 221– 236. Vincke, P. (1992), *Multicriteria Decision-Aid*, Chichester, New York, Brisbane, Toronto, Singapore: John Wiley & Sons.

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2005, volume 3410 of Lecture Notes in Computer Science**, pages 885–896, Berlin Heidelberg,** 2005. Springer-Verlag. [8] Malek Rahoual, Boubekeur Kitoun, Mohamed-Hakim Mabed, **Vincent Bachelet, and F´ethia** Benameur. Multicriteria genetic algorithms for the vehicle routing problem with time windows. In de Sousa [2], pages 527–532. [9] Marius M. Solomon and Jacques Desrosiers. Time window constrained routing and scheduling problems. Transportation Science**, 22(1):1–13, February 1988.** 7

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[9]H.Owladeghaffari, M. Sharifzadeh, K.Shahrair and E.Bakhtavar: Rock Engineering Modeling based on Soft Granulation Theory. In 42nd U.S. Rock Mechanics Symposium, San Francisco, CD-ROM, 2008. [10]H.Owladeghaffari, K.Shahriar and W. Pedrycz: Graphical Estimation of Permeability Using RST&NFIS. In NAFIPS 2008, New York, 2008. [11]H. Owladeghaffari, M.Sharifzadeh and W. Pedrycz: Phase Transition in SONFIS&SORST; In The Sixth International Conference on Rough Sets and Current Trends in Computing;C.-C. Chan, J.W. Grzymala-Busse, W.P. Ziarko (Eds.) LNAI 5306, pp. 339 –348, Akron, Ohio, USA, 2008.

<image> <image> HDPITM+ITM can produce φ, which provide lower ∆, under this strategy. However, HDPITM+ITM performance under the condition with low user interest and low tag ambiguity, is still inferior to HDP+LDA. This is simply because their structures are still the same to those of HDP and HDPITM respectively. ACM Journal Name, Vol. x, No. y, zz 2010.

Last accessed: May 2007 [21] *Fuzzy Logic Toolbox***, Matlab Help Files, MathWorks** [22] Marwala T. Artificial Intelligence Methods.,2005 http://dept.ee.wits.ac.za/_marwala/ai.pdf Last accessed: may 2007 [23] Ha K, Cho S, Maclachlan D. *Response Models Based on Bagging* Neural Networks, **Journal of Interactive Marketing Volume 19,** Number 1, 2005, pp17-33. [24] Pelckmans K, Suykens JAK, Van Gestel T, De Brabanter J, Lukas J, Hamers B, De Moor, Vandewalle J. **LS-SVMlab Toolbox User's** Guide**, Version 1.5, Department of Electrical Engineering,** Katholieke Universiteit Leuven, Belgium, 2003. http://www.esat.kuleuven.ac.be/sista/lssvmlab/ Last accessed: 30 April 2007

<image> Figure 1: Example. (a) A Forney graph. (b) Corresponding extended graph. (c) **Loops** (in bold) included in the 2-regular partition function. (d) **Loops (in bold and** red) not included in the 2-regular partition function. Marked in red, the triplets associated with each loop. Grouped in gray squares, the loops considered in different subsets Ψ of triplets: (d.1) Ψ = {c, h}, (d.2) Ψ = {e, l}, (d.3) Ψ = {**h, l**}, (d.4) Ψ = {c, e} and (d.4) Ψ = {c, e, h, l} **(see Section 2.2).** As an example, Figure 1a shows a small Forney graph and Figure **1c shows seven loops** found in the corresponding 2-regular partition function. ## 2.1 Computing The 2**-Regular Partition Function Using Perfect Matching** In Chertkov et al. (2008) it has been shown that computation of Z∅ **can be mapped to a** dimer/matching problem, or equivalently, to the computation of the sum of all weighted perfect matchings within another graph. A perfect matching **is a subset of edges such that**

[5] Driankov, Dimiter; Hellendoorn, Hans; and Reinfrank, Michael, An Introduction to Fuzzy Control. Springer, Berlin/Heidelberg, 1993. [6] K. Atanassov, D. Stoyanova, *Remarks on the Intuitionistic Fuzzy Sets. II*, Notes on Intuitionistic Fuzzy Sets, Vol. 1, No. 2, 85 - 86, 1995. [7] Coker, D., *An Introduction to Intuitionistic Fuzzy Topological Spaces*, Fuzzy Sets and Systems, Vol. 88, 81-89, 1997. [Published in the author's book: A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition), Am. Res. Press, Rehoboth, 2005.]

<image> ## 3.1 Fitness Distance Correlation Of Nd-Landscapes To estimate the difficulty to search in these landscapes we will use a measure introduced by Jones [21] called *fitness distance correlation* (FDC). Given a set F = {f1, f2**, ..., f**m} of m individual fitness values and a corresponding set D = {d1, d2**, ..., d**m} of the m distances to the global optimum, FDC is defined as: $$F D C={\frac{C_{F D}}{\sigma_{F}\sigma_{D}}}$$ where: $$C_{F D}={\frac{1}{m}}\sum_{i=1}^{m}(f_{i}-{\overline{{f}}})(d_{i}-{\overline{{d}}})$$ is the covariance of F and D and σF , σD, f and d are the standard deviations and averages of F and D. Thus, by definition, FDC stands in the range [−1, 1]. As we hope that fitness increases as distance to global optimum decreases, we expect that, with an ideal fitness function, FDC will assume the value of −1. According to Jones [21], problems can be classified in three classes, depending on the value of the FDC coefficient:

<image> <image> <image> average(D) = average(D1) + **average**(D2) and σ(D) = pσ 2(D1) + σ 2(D2) where σ is the standard deviation. The convolution product of two normal (resp. χ 2, Poisson) distributions is a normal (resp. χ 2, Poisson) distribution. Concatenation is commutative, so it is simple to concatenate a number of small landscapes. Hence, we can tack together many small ND-Landscapes generated exhaustively to obtain a bigger one with known neutral degree distribution. Moreover, it has been proven by Jones [21] that the FDC coefficient is unchanged when multiple copies of a problem are concatenated to form a larger problem. ## Conclusion This paper presents the family of ND-Landscapes as a model of neutral fitness landscapes. Most of the academic fitness landscapes

7. Donald Nute. Topics in Conditional Logic. Reidel Publishing Company, Dordrecht, 1980. 8. Mikhail Sheremet, Dmitry Tishkovsky, Frank Wolter, and Michael Zakharyaschev. Comparative similarity, tree automata, and diophantine equations. In Geoff Sutcliffe and Andrei Voronkov, editors, LPAR 2005, volume 3835 of Lecture Notes in Computer Science, pages 651-665. Springer, 2005. 9. Mikhail Sheremet, Dmitry Tishkovsky, Frank Wolter, and Michael Zakharyaschev. A logic for concepts and similarity. J. Log. Comput., 17(3):415-452, 2007. 10. Mikhail Sheremet, Franck Wolter, and Michael Zakharyaschev. A modal logic framework for reasoning about comparative distances and topology. submitted, 2008. 1. Robert Stalnaker. A theory of conditionals. In N. Rescher (ed.), Studies in Logical Theory, American Philosophical Quarterly, Monograph Series no.2, Blackwell, Oxford, pages 98-112, 1968.

... <constraints nbConstraints="5"> <constraint name="C0" arity="2" scope="V0 V1" reference="P0"> <parameters> V0 V1 </parameters> </constraint> <constraint name="C1" arity="2" scope="V0 V3" reference="P1"> <parameters> V3 V0 2 </parameters> </constraint> <constraint name="C2" arity="2" scope="V0 V2" reference="P2"> <parameters> V2 V0 2 </parameters> </constraint> <constraint name="C3" arity="3" scope="V1 V2 V3" reference="P3"> <parameters> V1 2 V2 V3 </parameters> </constraint> <constraint name="C4" arity="2" scope="V1 V4" reference="P0"> <parameters> V1 V4 </parameters> </constraint> </constraints> </instance> Figure 6: Test Instance in intention (continued)

... <constraint name="C4" arity="3" scope="X1 X4 X7" reference="global:weightedSum"> <parameters> [ { 1 X1 } { 1 X4 } { 1 X7 } ] <eq/> 15 </parameters> </constraint> <constraint name="C5" arity="3" scope="X2 X5 X8" reference="global:weightedSum"> <parameters> [ { 1 X2 } { 1 X5 } { 1 X8 } ] <eq/> 15 </parameters> </constraint> <constraint name="C6" arity="3" scope="X0 X4 X8" reference="global:weightedSum"> <parameters> [ { 1 X0 } { 1 X4 } { 1 X8 } ] <eq/> 15 </parameters> </constraint> <constraint name="C7" arity="3" scope="X2 X4 X6" reference="global:weightedSum"> <parameters> [ { 1 X2 } { 1 X4 } { 1 X6 } ] <eq/> 15 </parameters> </constraint> <constraint name="C8" arity="9" scope="X0 X1 X2 X3 X4 X5 X6 X7 X8" reference="global:allDifferent" /> </constraints> </instance> Figure 8: The 3*-magic square* instance (continued)

[Walsh 2007] Walsh, T. 2007. Breaking value symmetry. In 13th Int. Conf. on Principles and Practices of Constraint Programming (CP-2007). [Zhang 1996] Zhang, J. 1996. Constructing finite algebras with FALCON. *Journal of Automated Reasoning* 17(1):1– 22.

<image> data set are presented in Figure 1. Satisfiable problems are harder **to predict for** both rand and bmc **datasets, due to the abrupt way in which search terminates** with open nodes. ## 3.2 Search With Restarts With restarts, we have to use smaller observation windows to give a prediction early in search as many early restarts are too small. Figure 2 compares the quality of prediction of LMP for the 3 different datasets. The quality **of estimates** <image> improves with the bmc **data set when restarts are enabled. We conjecture this is** a result of restarts before the observation window reducing noise. In order to see if predictions from previous restarts improve the quality of prediction, we opened an observation window at every restart. The window size is max(1000, 0.01·s) and starts after a waiting period of max(500, 0.02·s), when